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Cholesky numerical stability: inverse transform #356

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Cholesky numerical stability: inverse transform #356

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21ec0e0
Improve numerical stability of Cholesky invlink
penelopeysm Nov 30, 2024
571aefa
Simplify further
penelopeysm Nov 30, 2024
81bedf2
Use logcosh
penelopeysm Nov 30, 2024
f2b58cd
Swap over one more occurrence of logcosh
penelopeysm Nov 30, 2024
f2987eb
Update Stan documentation link
penelopeysm Nov 30, 2024
72599f7
Simplify loop in _logabsdetjac_inv_chol
penelopeysm Dec 1, 2024
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16 changes: 5 additions & 11 deletions src/bijectors/corr.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -353,7 +353,7 @@ function _inv_link_chol_lkj(Y::AbstractMatrix)
for i in 1:(j - 1)
z = tanh(Y[i, j])
W[i, j] = z * exp(log_remainder)
log_remainder += log(2 / (exp(Y[i, j]) + exp(-Y[i, j])))
log_remainder -= LogExpFunctions.logcosh(Y[i, j])
logJ += log_remainder
end
logJ += log_remainder
Expand All @@ -380,7 +380,7 @@ function _inv_link_chol_lkj(y::AbstractVector)
for i in 1:(j - 1)
z = tanh(y[idx])
W[i, j] = z * exp(log_remainder)
log_remainder += log(2 / (exp(y[idx]) + exp(-y[idx])))
log_remainder -= LogExpFunctions.logcosh(y[idx])
logJ += log_remainder
idx += 1
end
Expand Down Expand Up @@ -460,13 +460,8 @@ function _logabsdetjac_inv_corr(Y::AbstractMatrix)
K = LinearAlgebra.checksquare(Y)

result = float(zero(eltype(Y)))
for j in 2:K, i in 1:(j - 1)
@inbounds abs_y_i_j = abs(Y[i, j])
result +=
(K - i + 1) * (
IrrationalConstants.logtwo -
(abs_y_i_j + LogExpFunctions.log1pexp(-2 * abs_y_i_j))
)
@inbounds for j in 2:K, i in 1:(j - 1)
result += (K - i + 1) * (-LogExpFunctions.logcosh(Y[i, j]))
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end
return result
end
Expand Down Expand Up @@ -495,8 +490,7 @@ function _logabsdetjac_inv_chol(y::AbstractVector)
@inbounds for j in 2:K
tmp = zero(result)
for _ in 1:(j - 1)
z = tanh(y[idx])
logz = 2 * log(2 / (exp(y[idx]) + exp(-y[idx])))
logz = -2 * LogExpFunctions.logcosh(y[idx])
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The name logz is a bit meaningless now I guess 🙂

result += logz + (tmp / 2)
tmp += logz
idx += 1
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